Problem: Simplify the following expression: $t = \dfrac{7p^2 - 84p + 189}{p - 9} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $7$ , so we can rewrite the expression: $ t =\dfrac{7(p^2 - 12p + 27)}{p - 9} $ Then we factor the remaining polynomial: $p^2 {-12}p + {27} $ ${-9} {-3} = {-12}$ ${-9} \times {-3} = {27}$ $ (p {-9}) (p {-3}) $ This gives us a factored expression: $\dfrac{7(p {-9}) (p {-3})}{p - 9}$ We can divide the numerator and denominator by $(p + 9)$ on condition that $p \neq 9$ Therefore $t = 7(p - 3); p \neq 9$